Journal of Rese arch of the National Bureau of Standards Vol. 59, No.4, October 1957 Research Paper 2795
Speed of Sound in Water by a Direct Method 1 Martin Greenspan and Carroll E. Tschiegg
The speed of sound in distilled water wa,s m easured over the temperature ra nge 0° to 100° C with an accuracy of 1 part in 30,000. The results are given as a fifth-degree poly nomial and in tables. The water was contained in a cylindrical tank of fix ed length, termi nated at each end by a plane transducer, and the end-to-end time of flight of a pulse of sound was determined from a measurement of t he pulse-repetition frequency required to set the successive echoes into t im e coincidence.
1. Introduction as the two pulses have different shapes, the accurac.,' with which the coincidence could be set would be The speed of sound in water, c, is a physical very poor. Instead, the oscillator is run at about property of fundamental interest; it, together with half this frequency and the coincidence to be set is the density, determines the adiabatie compressibility, that among the first received pulses corresponding to and eventually the ratio of specific heats. The vari a particular electrical pulse, the first echo correspond ation with temperature is anomalous; water is the ing to the electrical pulse next preceding, and so on . only pure liquid for which it is known that the speed Figure 1 illustrates the uccessive signals correspond of sound does not decrcase monotonically with ing to three electrical input pul es. The input pulses temperature. fall halfway between the pulses for which the coinci There is also a practical interest in c in that water dence is set, so that they do not tend to overload is used as a standard liquid for the calibration of the amplifier or distort the oscill oscope traces. The instruments that measure the speed of sound in period of the oscillator, when properly se t, multi liquids automatically, both in the laboratory and in plied by twice the length of Ul e tank, is the speed of the field. In fact, it was in connection with the cali sound in the sample. bration of such "velocimeters" [1] 2 that our interest The oscilloscope trace actually looks like that in this work was first aroused. In the first place, shown in the in se t (fig. 1). The firs t cycle corre the available data scatter widely, as recent sum sponds to sound reHected from the inner faces only maries [2 , 3] clearly show. In many cases, the di s of the transducers, whereas the succeeding cycle crepancies far exceed the claimed accuracy or at correspond to sound reflected. one or more times from least the precision of the methods, even when the an outer face. Therefore, the coincidence is set by methods compared are the same. In the second maximizing the peak on eitllcr the first or second place, there exists no set of data that gives a smooth balf-cycle; the same result is obtained in either case variation with temperature over any considerable but the second half cycle is easier to use because it range. In particular, the best of these data yield is bigger. What we are mea uring h ere is the speed calibration curves for OUT velocimeters which are corresponding to the fi1" t arrival of the signal ; in a badly curved instead of straight (as they should be), nondispersive liquid this is the same as the phase and about which the data scatter irregularly, but velocity. It is true that the coin cidence is made at a reproducibly. The results here presented are free of these objections. 2. Method At the top of figure 1 is a schematic of the appa ratus. The sample is confined in a tube of which the ends are plane, parallel, electroacoustic trans ducers, quartz crystals in this case. If the left-hand crystal, say, is excited by a short pulse from the blocking oscillator, the oscilloscope, which measures the voltage on tne right-hand crystal, will show a received pulse and a series of echoes, as indicated n in idealized form on the line below (fig. 1). The pulse repetition frequency of the blocking oscillator is controlled by a sine-wave oscillator, and if this I frequency were adjusted so that each blocking oscil n lator pulse coincided with the first received pulse of the next preceding cycle, then the oscillator period I ~I would equal the time of flight of the pulse. However, n FIGURE 1. Schematic of method. I 1'bis work was supported in part by the Omce of Naval R esearch under contract NA-oTU"-7
3 . Appar a tus
3 .1. The Delay Line The disassembled delay line is shown in the photo graph, figure 2. The length of the tank i s about 200 mm, and the bore about 13 mm. The filling holes are sealed by plugs having T eflon gaskets; a small hole in one plug provides pressure.r elease. The tank is of a chromium steel 3 which, after heat treatmen t, takes a good optical fini sh. . Because this steel is not so corrosion r esistant as the nickel chromium stainless steels, the bore of the tank was heavily gold plated. The ends of the tank are optically flat and parallel to within less than 1 f.1. To these ends are carefully wrung the 0.8-mm thick x-cut quartz crystals, which also are optically flat. The caps, when bolted on, clamp the crystals through neoprene O-rings. A FIGURE 3. Schematic oj one end of the tank, showing th e crystal coaxial cable passes through a seal in each cap, and and cap assembly. the center conductor makes contact with the outer 1. 'rank; 2. cap; 3. pl ug sealed with Teflon O-ring (thermocouple pasSf'S t hro ugh pressure relief tu be); 4. quartz crystal wrun g on to end of tank (springs (hot) electrode of the crystal through a light spring. make conta ct to electrodes) ; 5, neoprene O·ring; and 6, coaxial cable. The outer electrode is a 9 mm circle of aluminum backed pressure-sensitive adhesive tape. The inner was th e tank and heat-treated together with it. (ground) electrode is of fired-on gold and is about From these data, the length of the sound path is 12 mm in diameter. Contact is made through a known to better than 2 parts in 105 at any tempera light gold-plated helical spring which touches the ture between 0° and 100 0 C. It is, of course, electrode around the edge and bears on a shoulder necessary that the crystals be wrung down with machined into the bore. The inner electrodes and great care so that the fringes disappear all around springs are unnecessary if the sample has high con the periphery, to achieve this accuracy. The clamp ductivity or a high dielectric constant; they are ing gaskets must bear direc tly over the contacting usually omitted for water and aqueous solutions of surface and not spread out over the unsupported salts. Figure 3 is a schematic drawing of one end area, else the crystal will benel. With these pre of the assembly. cautions, the delay line may be disassembled and The length of the tank was measured at 20° C, reassembled repeatedly with reproducible results. and the coefficient of thermal expansion of the steel If the crystals have been properly wTung on and was measured on a sample cut from the same bar as clamped, they cannot be removed by hand after 3 F irtb-Sterling typelB-440A. several days, but must be soaked off. 250
'\- -- J 3 .2. The Electronics and poured, while still hot, into th e preheated tank. Although dis sol ved air has a negligible eff ect on the The electronic eircuils (fL g. 1) are, for the most speed of sound in water [4], it is desirable to exclude part, conventional. Howeve r, the oscillator and the air and so prevent possible bubble formation on the pulse-forming circuits must be exceptionally free of transducers. jitter. In addition, the o sc illatormus~ be provided The other two samples were vacuum distilled di with fine frequency control, so that it can be set rectly into the tank. The tank was placed in an icc within the r equired sensitivity of measurement, and bath and connected to a flask of di stilled water. it must be so stable that the frequency does not The system was then evacuated, and the water change during the counting time by enough to alter allowed to distill over at about 50° C. the count by more than one. The results of the three runs were the same wit,hin The blocking oscillator produces a pulse about 100 the errors of measurement; the data were, LhercJore, v high and 0.05 to 0.25 }.lsec wide. It is best driven combi ned. by a large, fast pulse sucl~ as is. gotten by differen.tia tion of a square wave derIved, m turn, from the sme 3.5. Technique wave generator.4 The jitter may be reduced further by means of a narrow band filter after the oscillator. The water bath was cooled to just above 0° C, The receiving circuit consists simply of a short and the heaters were operated at low power to sta length of low-capacitance cable, a wide band (5.5 bilize the temperature. (B elow room temperature ).I[c, in this case) amplifier of gain 100 to 1,000, and the refrigeration machine was rLLn continuously. ) a high-frequency type oscilloscope equipped with After the r eadings were taken, the power input to fast sweeps. The sweep is triggered from. the the heaters was increased, and so on until the tem oscillator through a variable delay; t h e necessary perature was just below 100° C. ,Vhen the tem delay time is abou t half the oscillator period. perature was stabilized, as indicated by the con stancy of the Mueller bridge reading and the near 3.3 Temperature Control and Measurement zero reading of the thermocouple galvanometer, the coincidence was set on the oscilloscope by one ob The delay line, suspended from its cables, is server and the frequency (doubled for convenience) deeply immersed in a 27 gal, well-insulated, water was measured by cO LLnting cycles for 10 sec (about bath. The bath is provided wi th 2 pump-type 75,000 co unts) by means of an electronic counter. stirrers, 3 heating coils, and a cooling coil connected At the same time, a nother observer balanced and Lo a small refrigeration unit. The temperature of read the Mueller bridge and read the thermoco uple tbe water adjusts itself so that the losses equal the galvanometer denection. power input to the heating coils, and various temper ,Vhile the temperature readings were being made, atures arc 0 b tained simply by varying the power inpu t. the coincidence was independently set a nd the re The temperature is, by t hi s means, easily held to sulting frequenc.v measured t hree times or more. wi thin less than 0.005 deg C for the in terval of time The various readings were always within the ± 1 required for the measurements, except that above countillherent error (e\Ten for different observers) 75° C, or so, the variation may become 0.02° or and the modal valu e was reco rded. This, divided 0.03 ° C; at the higher temperatures, however, tbe by 20 and multiplied by the length of the tank at t hermal coeffi cient of tbe speed of sound in water is the particular temperature, was taken as the speed rather low. of so und, c, correspondin'2; to the temperature, T , The temperature of Lhe bath water is measured obtained by calculation from the platinum ther with a platinum resistance thermometer and Mueller mometer and the thermocouple readings and the as Bridge. A differential th ermocouple has one junc sociated calibration data. All temperature calcula tion in the sample in the delay line, and one tied to tions were made to the nearest 0.001 ° C and the final the platinum thermometer; it passes through the result was rounded off to the nearest 0.01 ° C. pressure release tube (fig. 2). The thermocouple In order to insure that the coincidence was set on reading serves to indicate ,vhen the sample and bath the proper cycle, it was first set approximately, using water are substantially in thermal equilibrium, and the coarse frequency control, at a moderate sweep measurements are made when the discrepancy is less speed and low oscilloscope gain, so that the entire than 0.01 ° C (somewhat greater at the high temper pulse was visible on the screen . The sweep speed atures). The thermocouple and cralvanometer com was then increased while the delay was readjusted bination was calibrated for small temperature dif to keep the proper cycle centered. N ext, the gain ferences against the platinum resistance thermom was increased while the base line was moved off the eter so that small correcLions to the temperature screen to keep the point of extrem e deflection cen readings could be made. tered, and the amplitude was then adjusted to a maximum using the fine frequ ency control. 3.4. Samples The measurements here reported were made on 4. Results three separate samples of water. One sample was ordinary laboratory distilled water. This was boiled From readings taken at 83 temperatures between 0.14° and 99.06° C, the calculated values of the 4 The squ ar~- w a v e generator must be of the type that amplifies and thon clips the input sine \\l' avc. 'I'l le free-running, synchronized type is not suitable. speed of sound wcrefit.ted by the electronic com- 251 .06
.04 I. _ • . 0 2 - . . .- '""- ~ ' . . vi 0 .' ...J . ' . ~ - /:)2 - . 0 Vi w Q: -.04
-.06
0 10 20 30 40 50 60 70 eo 90 100 TEMPERATURE. °c
FIGURE 4. Deviations, r, of eq1wtion 1 from the data. putcr SEAC by the method of least squares, to a significant fig ures, so that on account of rounding-off fifth-degree polynomial, errors, the tabulated differences in some cases differ by one unit in the last decimal place from the dif (1) fer'ences of the tabulated values of c. It is believed (sec section 5) that the systematic errors do not The reduction in the residual sum of squares over a exceed 1 part in 30,000. The tables should, there fourth-degree polynomial, due to fitting the f-ifth fore, be used in the following manner. In table 2, degree term, was statistioolly significant at a prob linear interpolation should be performed to the ability level less than 0.005, and the deviations of nearest 0.01 m/s and the final result rounded off to the data from the fifth-degree polynomial showed no the nearest 0.1 m/s. The error will then not exceed statistically significant indication of lack of random one-half unit ill the last place, i. e., 0.05 m/s. Linear ness. The deviations are plotted against tempera interpolation in table 3 will yield errors that do not ture in figure 4. exceed 2 units (0.2 fps) in the last place. The values of a, in eq (1), for c in meters per second (m/s), and T in degrees C, are: ao= 1,402.736; a[ = 5 . Discussion 5.03358; a2= - 0.0579506; a3= 3.31636 X 10- 4 ; a4 = - Following is a list of the known possible sources 1.45262 X 10- 6 ; and a5=3.0449 X 10- 9 • The stand of error and an estimate of the upper limit of each ard deviation of the measurements is 0.0263 m/s, or error. about 17 ppm. Estimated standard deviations of the values of c predicted by eq (1) were calculated 5.1. Frequency for five representative temperatures. The results As already stated, the frequency was measured by are given in table l. counting cycles for 10 sec; the total count was about 75,000. The inherent error is ± 1 count, but TABLE l. E stimated standard deviation (s. d.) of values of c predicted by equation 1 in all cases the mode of at least three independent readings, of which, at worst, two were the same and Temperature s. d . the third different by one, was taken as the observed value. The counting error can thus be as great as ° C m/s ppm 1 part in 75,000, but as it is random, the effect on o 0. 0114 8.1 10 . 0065 4.5 the final results is negligible, as indicated in section 4. 50 . 0058 3.8 The 10-sec time base was obtained by division from 70 . 0062 4.0 100 .0145 9.4 a I-Me crystal oscillator which is stable to 2 parts in 107 per week, and which was compared with signals Table 1 and figure 4 make it clear that eq (1), from W, VV 01' from a local precision standard. The together with the listed constants, provides a satis errors due to inaccuracies in the time base are, factory interpolation formula, and the errors intro therefore, also negligible. duced by its usc are small relative to the possible 5 .2. Length of Path systematic errors of measurement (sec section 5). The values given in tables 2 and 3 were calculated The length of the tank across its polished ends at from eq (1) by SEAC. 20° C was determined within IlL, i. e., 5 ppm. Ther Table 2 gives the speed of sound in meters per mal expansion measurements were made at 20 °, 60°, second for each degree C from 0 to 100, and table 3 and 100° C; the lengths at intermediate tempera gives the speed of sound in feet per second at inter tures were calculated by quadratic interpolation. vals of 2 deg F from 32 ° to 212°. In each case, the The maximum absolute error in the thermal expan differences, which are listed for convenience in inter sion coefficient is estimated at 0.2 ppm; this accu polation, were calculated from a table having more mulates to 4 ppm at 0° C, and to 16 ppm at 100° C. 252 T A BLE 2. Speed of sound in water, metric units
l' c T c Ll. T c Ll. l' c A ------'" ------°C mls mls °e mls m!s °e mls mls °C mls mls 1, 400+ 1,400+ 1,500+ I, .500+ 0 2.74 ------25 97.00 2.71 50 42.87 1. 12 75 55.45 -0.01 I 7.71 4.97 26 99.64 2.64 51 43.93 1.07 76 55.40 -.05 2 ]2.57 4.86 27 '2.20 2.56 52 44.95 1. 02 77 55.3 1 -.09 -.]3 ~ 17.32 4.75 28 4.68 2.49 53 45.92 0.97 78 55.18 4 2l. 96 4.64 29 7.10 2.41 54 46.83 .92 79 55.02 -.17 5 26.50 4.53 30 9.44 2.34 55 47.70 .87 80 54.81 -.20 6 ~O. 92 4.43 31 II. 71 2.27 56 48.51 .82 81 54.57 -.24 I 7 3.1.24 4. ~2 32 13. 91 2.20 57 49.28 . 77 82 54.30 -.28 8 39.46 4.22 33 1605 2.14 58 50.00 .72 83 53.98 -.31 9 43.58 4.12 34 18. 12 2.07 59 50.68 .67 84 53.63 -.35 I 10 47.59 4.02 35 20. 12 2.00 60 51. 30 .63 85 53.25 -.39 II 51. 51 :1.92 36 22.06 1. 94 61 51. 88 .58 86 52.82 -.42 12 55.34 3.82 37 23.93 1. 87 62 52. 42 .53 87 52.37 -.46 13 59.07 3.73 38 25.74 1.81 63 52.91 . 49 88 51.88 -.49 14 62.70 3.64 39 27.49 1. 75 64 53.35 . 45 89 51.35 -.52
1.1 66.25 :3.0.1 40 29.18 1. 69 65 53.76 . 40 90 50. 79 -.56 16 69.70 3.4f> 41 30.80 1. 63 66 54.11 .36 91 50.20 - . 59 17 73.07 3.3, 42 32.37 1. 57 67 54. 4~ . 31 92 49.58 -.63 18 ifi.3.1) :J.28 43 33.88 1. 51 68 54.70 .27 93 48.92 -.66 19 79.55 3 . .1 9 44 35.33 1. 45 69 54.93 .23 94 48.23 -.69 I 20 82.66 3.11 45 36.72 I. 39 70 55. 12 . 19 95 47.50 -.72 21 85.69 3.03 46 3R06 1. 34 71 55.27 . 15 96 46.75 -.76 22 88.63 2.9.5 47 39.34 1. 28 72 55. :.i7 . 11 97 45.96 -.79 23 91.50 2.87 48 40.57 I. 23 73 55.44 .07 98 45. 14 -.82 99 44.29 -.85 24 94.29 2.79 49 41. 74 1.17 74 55.47 .03 I 25 97.00 2.71 50 42.87 I. 12 75 .):,),4.1 -.01 100 43.4 1 -. 88 1,400+ 1,.500+ 1. 500+ 1,500+ ------I
TM1L'E; 3. Speed of s01md in water, English 1U~its
T ..'> l' A T Ll. T ..'> _.-- -.------OF fps fps OF fps fps op fps fps OF fps fps 4, 600+ 4.900+ 5,000+ 5.000+ 30 80 25.7 9.4 130 76.2 3.3 180 99.2 -1.0 32 2.1 82 34.8 9.1 132 79.2 3.1 182 98.0 -1.2 :j4 20.3 18. I 84 43.7 8.8 134 82. I 2.9 184 96.7 -1.3 3(1 37.9 17.7 86 52.2 8.6 136 84. 2. 7 186 95.2 -1.5 38 55. 1 li.2 88 60.5 8.3 138 87.3 2.5 188 93.6 -1.6 40 71.9 16.8 90 68.5 8.0 140 89.6 2.3 190 91.8 -1.8 42 88.2 16. :l 92 76.2 7.7 142 9 1. 7 2.1 192 89.9 -1.9 44 104.1 15.9 94 83.6 7.4 144 93. G 1.9 194 87.9 -2.1 4n 119.6 15. 5 96 90.8 7.2 146 95.3 1.7 190 85.7 -2.2 48 134.6 1 ,i. I 98 97.7 6.9 148 96.9 1.6 198 83.4 -2.3 ,10 149.3 14. i 100 "'4.4 6.7 150 98.3 1.4 200 81. 0 -2.5 .12 163.6 14.3 102 10.8 6.4 152 99. ,I 1.2 202 78.4 -2.6 54 177. 5 13.9 104 17.0 6.2 154 100. ,I 1.0 204 75.7 -2.7 56 19l. 0 13.5 106 22.9 5. ~ 156 lOt. 4 0.9 200 72.9 -2.8 58 '4.1 13.1 108 28.6 5.7 158 102. 1 .7 208 70.0 -3.0 60 16.9 12.8 lIO 34.0 5.4 160 102.6 . 6 210 66.9 -3.1 62 29.3 12.4 112 39.2 5.2 162 103.0 .4 212 63.7 -3.2 64 4 1. 3 12.0 114 44.2 5.0 164 !O3.2 .2 66 53.0 J I. i 116 48.9 4.8 166 103.2 .0 68 64.4 I!. 4 11 8 53.5 4.5 168 !O3. I -.1 70 7,1.4 II. 0 120 57.8 4.3 liO 102.8 -.3 72 86. I 10.7 122 6J. 9 4. 1 172 102.4 -.4 74 96.4 10.4 124 65.8 3.9 174 101. B -.6 76 106 ..1 10.1 126 69.4 3.7 176 101. I -.8 78 116.2 9.8 128 72.9 3.5 178 100.2 -.9 80 125.7 9.4 lao in,2 3.3 180 99.2 - l.0 4,800+ 5.000+ 5.000+ ,i. 000+
Thus, the toLal uncertainty III the length of the attention to avoidance of clamping pressure too ncar tank is about 5 ppm at 20° 0, and increases with the unsupported arcas of the crystals, the crystals temperatU1'c both ways; at 0° 0 it becomes abou t might deflect enough to cause very sizable errors. 9 ppm and at 100° C, about 21 ppm. The present design makes it possible to disassemble The question arises as to how closely the length and reassemble the delay line repeatedly without of the sound path in the sample, i. e., the distance affecting the result by a detectable amount; this bctween the inner faces of the transducers, approxi holds true when the crystals normally used, which mates to the length of the tank across the ends to are 0.8 mm thick, are replaced by crystals 1.6 mm which the crystals are wrung. Experience with thiclc It, therefore, appears that errors produced developmental models showed that unless the assem by misplacement or deformation of the crystals arc bly \\:e['e very carefully made, with particular insignifican t. 253 5 .3. Setting the Coincidence constant at t llis valu e out to 70° C, and rises to about 35 ppm at 100° C. It is upon these considera As explained in section 2, it is believed that no tions that the recommendations for the use of the measurable errol' is introduced by the technique of tables in secLion 4 are based. maximization of the second half cyele of the received The values of c here reported are lower than those pulse. However, a word should be said about the of most other workers, in particular the value at effect of personal bias on the part of the opera to!'. 30° C is about 0.4 mls below that of D el Grosso, The operators report, to varying degrees, tendencies Smura, and Fougere [3], whose work with the ultra to adjust not only for maximum height of peak, but sonic interferometer is perhaps the most carefully also for maximum symmetry and sharpness of peale planned, executed, and analyzed work of this type Long experiment has convinced us that any of the to date. It was, therefore, felt desirable to perform three criteria lead to sensibly the same result, so an independent experiment using an apparatus a.ncl that although different operators weigh the three a method as difforent as possible from those of both criteria differently, they reproduce each o~h~r 's Del Grosso, et aI. , and ourselves. An apparatus settings so well that the discrepancies are neghgl?le was constructed with which itis possible to measure, relative to other sources of error. Tho assumptlOn as a function of distance, t lte phase on the axis of a is implicit that the errors of bias do not much exceed beam of progressive waves emitted b.\Ta small piston the discrepancies among individuals. like radiator. If the wave were plane, Lhe phase cp would vary linearly with distance x, and the phase 5.4. Temperature speed c would be 271'fx /cp where f is frequency. In the present case, the wave is not plane and the slopo The Mueller bridge with which the resistallce of of the curve 271'fx versus cp depends on x and on the the platinum thermometer was measured has a least geometry of t he arrang?ment. However, tl.lC theory count of 0.0001 ohm corresponding, for a 25-ohm .enables us to select a dIstance Xo of the reCBlver from thermometer Lo about 0.001 ° C. The bridge was the source such that for x>xo the departure of calibrated internally so that the indicated resistance 271'fdxldcp from c is as small as desired. in terms of the in ternal standard is correct to abou t "Five runs werc made in distilled waLm' at tempera 0.0002 ohm aside from temperature effects and slow tures between 15 ° and 25 ° C. The pripcipal un drifts in the arm ratio and in the zero. Allowing certainties are t hought to be first, one of about 40 for these, it is estimated that the bridge error does ppm corresponding to a possible errol' of 0.01 ° C in not exceed 0.005° C; errors in the calibration of the the temperature, and second, one of ahout 56 pJ;lm platinum thermometer itself and those due to heating related directl v to the inaccuracies of Lhe screw Wi Lh by the bridge current are much smaller. More im which the receiver displacement was measured. portant is the OlTor that arises from thermal gradients These arc independen t. However, ill Lhe worst case in the bath. On the assumption that this does not of the 5, the result differed from the value gotten exceed half the reading of the differential therm.o from table 2 b.\- only 27 ppm. The value of Del couple which, it will be recalled, measures the dif Grosso, et a1. [3] disagrees with that of table 2 b~T 272 ference between the temperature of the platinum ppm. element and that of the sample, an upper limit to the This work will be reported in detail else where. cOl'l'esponding uncertainty in the speed o~ sound, c, was calculated at various Lemperatures from the known thermal coefficient of c. This upper limit The authors are grateful to the perso nnel of the is zero at 74 ° C, where c is stationary and increases Engineering lIetrology Section and of the Length steadily in both directions, reaching about 25 ppm Section, in whose Laboratones the lengtll of the tank at 0° C, and about 14 ppm at 100° C. and its thermal expansion, respectively, were meas ured. Thanks arc particularly due to Josoph !vf . Cameron of the Statistical Engineering Section who 5 .5. Purity of Sample advised the authors on problems of data processing, Because the results obtained on ordinary labora and who performed the curve-fitting computations tory distilled water were indistinguishable from those onSEAC. obtained on the same water redistilled in vacuum 6. References directly into the apparatus, it is felt that the remain [1] Martin Greenspan and Carroll E. T schicgg, Sing-around ing impurities do not have a measurable effect. ultrasoni c velocimeter for liquids, Rcv. Sci. Instr. Several measurements made on local tap water gave (in press). results about 30 ppm higher than for distilled water. [2] R. A. McConnell and ' V. F. Mruk, Microaco ustic inter ferometer using 30 Mc pulses, J . Acoust. Soc. Amer. 27, 672 (1955). 5 .6. Over-all Accuracy [3 ] V. A. D el Grosso, E. J. Smura, and P . F . Fougere, Accur acy of ul trasonic interferometer determinations, NRL From the foregoing discussion it appears that the Report 4439, Naval Research Laboratory, Washington, major sources of errol' aTe Lhe uncertainties in the D. C. (Dec. 6, 1954) . [4] Martin Greenspan a nd Carroll E. Tschiegg, Effect of length of the path and in the temperature. Both of dissolved air on the speed of sound in water, J. Aconst-. these are temperature dependent; their sum is an Soc. Amer. 28, 501 (1956). upper limit to the total errol'. This is about 35 ppm at 0° C; it falls to 15 ppm at 40° C and is almost IV ASHINGTON, March 27, 1957 . 254